Correctly Modeling and Calculating Combustion Efficiencies In Fired Equipment David Schmitt, President Increase Performance, Inc. Tulsa, Oklahoma Fired equipment includes furnaces, fired heaters, fired boilers, supplementary fired boilers, and many other types of equipment. But for the purposes of reviewing how the calculations are accomplished and other factors that may affect the results of the modeling, we will use a fired reformer furnace as our example. All of the methods and issues discussed herein can be applied to any fired equipment. We will start with the combustion calculation which is necessary to calculate the properties of the flue gas, or the products of combustion as well as heat available from the combustion process. The chemical reaction formula for combustion is well known, but varies with the composition of the fuel being used, and can be very complicated if the fuel has many components. As an example, we look at a simple combustion of methane, CH 4 in Oxygen, O 2. CH 4 + 2O 2 --- > CO 2 + 2H 2 O The oxidant in most cases is normally air, but may be other gases such as Gas Turbine Exhaust, or other products of combustion. If it is air, the wet composition may be similar to the following, in mole %.
Nitrogen, N2 77.4560 Oxygen, O2 20.9108 Carbon Dioxide,CO2 0.0299 Water, O2 0.3772 Argon, Ar 0.9364 The actual composition of the oxidant will vary depending on the elevation, humidity and temperature at the site you are modeling. Even though Sulphur Dioxide and Carbon Monoxide are not normally considered to be in atmospheric air, your calculations should allow for these since the equipment may be using products of combustion from another piece of equipment. Dry air should not be used in combustion calculations because this rarely exists. For a combustion calculation, you need to know the composition of the fuel and the oxidant. To perform the combustion calculation you could use a computer software program such as WinBurn, or one of many calculators available on the internet. However, to make combustion calculations or test equipment for purposes of determining the efficiency of the combustion process, it is better to setup a simple excel work sheet to perform the calculations. For Liquid Fuels, the Excel sheet may be setup: Fuel # 1: Fuel Oil Resulting Composition; Component Name Wt% Fuel MW N2 O2 CO2 H2O Ar SO2 CO Sulphur 0.50 32.0640 0.000-0.998 0.000 0.000 0.000 1.998 0.000 Hydrogen 12.80 2.0158 0.000-7.937 0.000 8.937 0.000 0.000 0.000 Carbon 86.70 12.0112 0.000-2.664 3.664 0.000 0.000 0.000 0.000 Nitrogen 0.00 28.0160 1.000 0.000 0.000 0.000 0.000 0.000 0.000 Oxygen 0.00 32.0000 0.000 1.000 0.000 0.000 0.000 0.000 0.000 Water 0.00 18.016 0.000 0.000 0.000 1.000 0.000 0.000 0.000 Total 0.0000-3.3307 3.1768 1.1439 0.0000 0.0100 0.0000 Lower Heating Value, Btu/lb 18,390 Fuel Specific heat, Btu/lb- F 0.0000 Atomizing Medium MECH MECH (Mechanical), STM (Steam), or AIR
Air/Steam Pressure, psig 0.0000 Injection Rate, lb/lb 0.0000 Fuel Fuel # 1 Units Flow 1,393.000 lb/hr Temperature 60.00 F Heat Avail. From Fuel(Datum: 60 F), Btu/hr 0 Air/Fuel Ratio, lb/lb @ 0 % Ex. Air 14.4595 Excess Air, % 0.450 Air Flow, lbs/hr 20,233 Fluegas Flow, lbs/hr 21,626 Heat Avail. From Combustion of Fuel, Btu/hr 25,617,270 Notice that with Liquid Fuels, the Lower Heating Value is normally determined by laboratory testing and so it need not be calculated on this sheet, and is an input by user. For a Gas Fuel, the Excel sheet may be setup:
In the Excel tables above, we have columns for the resulting composition factor. In these columns, if the molecule is not changed by the reaction, the factor is simply a 1.0 in the appropriate column. But for the Methane molecule, since the chemical reaction formula indicates it takes two molecules of O 2 for the reaction, then the factor is two molecules of Oxygen/one molecule of CH 4 or 2*32/16.042 and it is negative because it eliminates the O 2 molecule. Likewise factor in the CO2 column for CH4 would be one molecule of CO 2 /one molecule of CH 4 or 44.01/16.042. All of the remaining rows and columns are populated in a similar manner. The table may have as many or as few as the composition for the particular fuel.
The total of each column in the table would be equal to the sum of the weight fraction of the component times the factor. For the heat available from the combustion, we are using the LHV values, which are typical for Fired Heater efficiency calculations, where for boilers the HHV values are typically used. The Air/Fuel Ratio, lb/lb @ 0% Excess air is the absolute value of the ratio of the O2 Factor/Weight fraction of O2 in the oxidant. So if we use the Wet Air composition from above, we can create a table for the oxidant or combustion air similar to below: Combustion Air: Component Mole % Wt Frac Air MW Air Temp, F 310.380 N2 77.7456 0.7529 28.016 Air Enth, Btu/lb 60.698 O2 20.9108 0.2313 32.000 Air Heat, Btu/hr 21,283,821 CO2 0.0299 0.0005 44.010 H2O 0.3772 0.0023 18.016 Ar 0.9364 0.0129 39.950 SO2 0.0000 0.0000 64.060 CO 0.0000 0.0000 28.010 Air Flow, ACFM 119,753 Total 99.9999 28.928 The weight fractions may be calculated by dividing the product of the component moles times the molecular weight/sum of all the moles multiplied by the molecular weights. The excess air % is an expression used to describe the additional air above that is required for stoichiometric combustion on a weight basis. Another way to describe this excess air is by wet or dry volume of O 2 % in the products of combustion (fluegas). Most handheld measuring devices measure the dry volume %, where many mounted devices measure the wet volume %. To see what a resulting value of O 2 is present in the fluegas, we need to create another table similar to below: Fluegas: Component Lbs Wt Frac Mole % N2 13.7035 0.7154 71.0958 O2 0.4152 0.0217 1.8858 Dry O2 % 2.2842 Wet O2 % 1.8858 CO2 2.6408 0.1379 8.7218 H2O 2.1619 0.1129 17.4423 Ar 0.2348 0.0123 0.8543
SO2 0.0000 0.0000 0.0000 CO 0.0000 0.0000 0.0000 Total 19.1562 1.0000 100.0000 Flow, lb/hr 369,964 Temp, F 1650 Enthalpy, Btu/lb 460.85 For N2 component burning the gas fuel in above table, Lbs Factor = 0.0328 + 0.7529 * 16.3614*(1 + 10.970/100) = 13.7035, and similar for other components. And then using these factors, the weight fraction and mole % can be calculated. Of course, you could calculate based on a measured O 2 such as when testing a furnace, or if you have your tables set up as above, simply change the excess air until the Measured O 2 and calculated O 2 are equal. If you have multiple fuels, just add fuel tables for each fuel; then add resulting composition factors to get the mixed fuel results. Now that we have reviewed how to do the combustion calculations, we know if we get the fuel compositions and the fuel flow, we can calculate how much heat is released along with the flue gas flow and composition, once we determine the excess air or Oxygen in the fluegas. Traditionally, this is done by taking a sample in the furnace stack. While this indeed will give you an overall assessment of the furnace operation, it will not help you determine if there are combustion problems, nor will it necessarily tell you what the correct efficiency is for the unit. Rather than use an example of a simple fired heater, let s take as our example a reformer system that is typical of many in the hydrogen and ammonia plants. This example will help us see all the pitfalls in performing combustion and efficiency calculations. A schematic of our example is as shown below.
It is important that all burners be on during a field test for combustion and efficiency. If burners are turned off, they should be repaired as necessary and re lit prior to testing. In this example, we have a reformer fired with two fuels, and preheated air in the arch burners. The tunnel burners are fired with one fuel and ambient air. The superheater burners are fired with one fuel but with preheated air, and the auxiliary boiler is also fired with one fuel and preheated air. On the day of our test, the ambient temperature was 60 F with a relative humidity of 40% and the plant is at a 1200 foot elevation. Using this data with standard air, we calculate the wet air composition to be as follows. Air: Component Mole % Wt Frac Air MW N2 77.4714 0.7512921 28.016 O2 20.8371 0.2308068 32.000 CO2 0.0298 0.000454 44.010 H2O 0.7286 0.0045437 18.016 Ar 0.9331 0.0129035 39.950 SO2 0.0000 0 64.060 CO 0.0000 0 28.010 Total 100.0000 28.889 Our physical examination and walk through of the unit, revealed that the unit has 260 tubes, and the tube seals at the arch consist of a plate with a hole 1/8 larger than the tube OD, so we must take into account the possible leakage air in this area. In a plant such as this the FD fan
operation would normally be controlled based on the O 2 reading at Point 1, at the tunnel exits. However, it is clear from examination of this design, that the arch burners could be short on air, yet the tunnel exit O 2 reading may indicate a sufficient excess air because if there are two independent sets of burners, the sample point must be made at a location between them. So even though the control room indication was that the reformer was operating with a 2.1 % O 2 at exit temperature of 1900, sampling at Point 1 in the wall of the radiant section, the results were zero % oxygen and combustibles were present. The ID fan is being operated to maintain a 0.2 W.C. at the reformer arch. This reformer has two fuels, natural gas plus purge or off gas. And the air is preheated to 532 F. Therefore we set our Excel worksheet up with a table for two fuels and the resulting combustion calculation would be similar to below. It is important to note that the actual excess air would be negative, since the sampling result indicated no O 2 present, and it cannot make a determination on how much additional O 2 is required. The second thing to note is that the calculated seal leakage air, where it may be present in the radiant section, it is not entering the fire zone from the correct location, i.e., through the burner tile, so it does not promote good
combustion. Even though our calculator will handle a negative excess air, or incomplete combustion, we set the Excess Air to zero for the arch burners. With the fuel flow reading to the tunnel burners known and the O 2 reading at the exit, we can now perform the tunnel burner combustion calculation with the following result. But since we know that the Arch Burners are operating with no excess air, which is not the same as the Tunnel Burners, we have to introduce an overall heat & mass balance sheet to determine the excess air in the Tunnel Burners. This new sheet might look like the following: So now we can adjust the excess air in the Tunnel Burners until the total leaving the tunnels is equal to the measured O 2.
If the only data looked at was the reformer outlet, Point 2, Dry Volume O2 of 2.1 %, then the conclusion would be Everything is fine, but we now know that the complete combustion is not occurring in the designed flame zone for the Arch Burners, as well as all the combustion air is not entering at the flame zone as it should. This poor combustion will result in poor radiant flux distribution and may shorten the life of tubes and catalyst. Also, operating the Tunnel Burners with 186.2 % Excess Air causes these burners to be operating very inefficiently.
Our next sample point is just downstream of the Superheater Burners, where we have an O2 reading of 2.25 % and a temperature of 1390 F. Once again, we cannot directly determine this temperature or the excess air in the combustion without adding to our heat & mass balance sheet. We adjust the firing conditions on the Superheater Burners until we meet our targets on the Heat balance Sheet. And the resulting combustion calculation for the Superheater Burners is as follows:
Efficient operation of these burners would be with 10% excess air, but they are operating with 18.2 % excess air. Point 10 of our field measurements is the fluegas returning from the Auxiliary boiler, which has a Dry Volume % O 2 of 3.5 and a temperature of 676.7 F. This is a straight forward combustion calculation as shown below.
The efficiency of the Auxiliary Boiler is 128284536/154481064 *100 = 83.0 % and could be improved by adjusting burners to a lower excess air. Now we add to our heat and mass balance to determine the fluegas after the mixture.
Our next sample point is Point 4 entering the Air Preheater, which has an O2 reading of 2.8 % and a temperature of 643 F. Examination of our heat and mass balance indicates that this O 2 reading should have been 2.540 %, which tells us that there has been ingress of tramp air between Point 3 and Point 4. Physical examination of the unit reveals that there are no port seals on the interconnecting pipes, and a tissue test shows that air is entering the convection at these locations. We can expand our heat and mass balance to determine the amount of the air leakage.
This is not a great amount of leakage, but does have an associated cost in loss of energy, and the repair will have a relatively short payout. The Air Preheater on this sample analysis is a regenerative, rotary type, which when in new condition with new seals has an inherent air bypass (leakage) from the high pressure, Forced Draft (FD), side to the low pressure, Induced Draft (ID), side, therefore we expect to see a leakage bypass of over 10 % by volume. The actual bypass leakage is easy to calculate using our heat and mass balance sheet, with the O 2 reading known to be 2.8 % at the inlet and 5.76 % at outlet. We also measure a fluegas exit stack temperature of 252 F.
We can see from the heat and mass balance that the bypass air leakage is 19.92 %, or twice what it should be. We can also see that our air preheater balance is a little off, by 2.31 % which is not unusual since heat loss to the atmosphere has not been taken into account. To recap the findings from this sample furnace test to demonstrate combustion, efficiency calculations, and heat and mass balance techniques, the following is a brief list of problems uncovered: 1) The lack of reformer tube seals is allowing tramp air to enter radiant section 2) The primary arch burners are not receiving sufficient air for complete combustion 3) The tunnel burners are being operated with excessive excess air 4) The superheater burners are being operated with excessive excess air 5) The auxiliary boiler burners are being operated with excessive excess air 6) The second convection section has no port seals and this allows ingress of tramp air 7) There is excessive air bypass in the air preheater 8) The ID fan is being overloaded due to excessive excess air in the Tunnel, SH, and Aux. Boiler, tramp air ingress, and air bypass in air preheater 9) The FD fan is being overloaded due to excessive bypass air in the air preheater With all the combustion and mass and heat balance calculations complete, we can now look at our results. We can use the methods described in API 560 to calculate the efficiencies. Fuel Efficiency = Heat Absorbed/Total Heat From Fuel * 100 Net Thermal Efficiency = ((Heat From Fuel + Air Heat + Fuel Heat) (Set. Loss + Stack Loss)) / (Heat From Fuel + Air Heat + Fuel Heat)
We should note here that these efficiency calculations do not take utilities or fan power into account. The amount of energy used to drive the fans is estimated roughly above. This overall efficiency doesn t tell us about the poor combustion in the primary reformer and doesn t account for the loss of tube or catalyst life. The enthalpy calculations used herein are based on our internal calculators, but if you don t have any of the equations, you can use curve fits of the curves in API 560, Figure G6 and G7, reproduced below.
If possible, it is also desirable to calculate the heat absorbed in the fired equipment to compare against the combustion calculations to assure an accurate heat balance has been achieved.